1. TOPIC 4 Net Present Value and Other Investment Criteria
4.2. The Payback Rule
4.3. The Discounted Payback
4.4. The Average Accounting Return
4.5. The Internal Rate Of Return
4.6. The Profitability Index

2. 4.1. Net present value
Suppose you buy a run-down house for $ and spend another $ on getting it fixed up. Your total investment is $ When the works are completed, you find that it’s worth $ The market value ($60.000) exceeds the cost ($50.000) by $

3. 4.1. Net present value
Net present value (NPV) is the difference between an investment’s market value and its cost.
We will estimate NPV as the difference between the present value of the future cash flows and the cost of the investment.
This procedure is often called discounted cash flow (DCF) valuation.

4. 4.1. Net present value
Suppose we believe the cash revenues from our business will be $ per year. Cash costs will be $ per year. We will wind down the business in eight years. The plant, property, and equipment will be worth $2.000 as salvage at that time. The project costs $ to launch. We use a 15% discount rate.
Is this a good investment?

5. 4.1. Net present value Project cash flows ($000)
Time (years) ____0_____1_____2_____3_____4_____5_____6______7_____8
Initial costs
Inflows
Outflows
Net inflow
Salvage
Net cash flow
______________________________________________________________________________

6. 4.1. Net present value
Present value =
= x (1-1/1,158 ) / 0, / 1,158 =
= 6.000x4, / 3,0590 = =
We compare this to the $ estimated cost, we see that the NPV is:
NPV = =

7. 4.1. Net present value
This is not a good investment. Based on our estimates, taking it would decrease the total value of the stock by $2.422.
The Goal of financial management is to increase share value.
Net present rule: an investment should be accepted if the net present value is positive and rejected if it is negative

8. 4.1. Net present value
Suppose we are asked to decide whether or not a new consumer product should be launched. Based on project sales and costs, we expect that the cash flows over the five-year life of the project will be $2.000 in the first two years, $4.000 in the next two, and $5.000 in the last year. It will cost about $ to begin production. We use a 10% discount rate to evaluate new products. What should we do here?

9. 4.1. Net present value
Present value =
= 2.000/1, /1, /1,103 +
/1, /1,105 = = = =
NPV = = 2.313

10. 4.2. The Payback Rule
Payback period is the amount of time required for an investment to generate cash flows sufficient to recover its initial cost.
The initial investment is $ After the first year, the firm has recovered $30.000, leaving $ The cash flow in the second year is exactly $20.000, so this investment “pays for itself” in exactly two years. The payback period is two years. If we require a payback of three years or less, then this investment is acceptable

11. 500-100-200=200 we need to recover in 3rd year
4.2. The Payback Rule
Year ___0________1_________2_________3_________4
-50, , , , ,000
Based on the payback rule, an investment is acceptable if its calculated payback period is less than some prespecified number of years.
Year ___0________1_________2_________3
=200 we need to recover in 3rd year
200/500=0,4 The payback period is 2,4 year

12. 4.2. The Payback Rule Year A B C D E
________________________________________________

13. 4.2. The Payback Rule Analyzing The Rule Consider the two
investments, Long and
Short. The payback on
Long is 2+(50/100)=
2,5 years, and the
payback on Short is 1+(150/200)= 1,75 years.
With the cutoff of two years, Short is acceptable and Long is not.
Year
Long
Short
-250 1
100 2
200 3 4

14. 4.2. The Payback Rule
Suppose again that we require a 15% return on this type of investment. We can calculate the NPV for these two investments.
NPV(Short) =
(100/1,151) + (200/1,152) = -11,81
NPV(Long) =
x (1-1/1,154)/0,15 = 35,50

15. 4.2. The Payback Rule
Advantages and Disadvantages of the Payback Period Rule
Advantages
1.Easy to understand.
2.Adjust for uncertainty of later cash flows.
3.Biased towards liquidity.

16. 4.2. The Payback Rule
Disadvantages
1.Ignores the time value of money.
2.Requires an arbitrary cutoff point.
3.Ignores cash flows beyond the cutoff date.
4.Biased against long-term projects, such as research and development, and new projects.

17. 4.3. The Discounted Payback
Discounted payback period is the length of time required for an investment’s discounted cash flows to become equal to its initial cost.
Based on the discounted payback rule, an investment is acceptable if its discounted payback is less than prespecified number of years

18. 4.3. The Discounted Payback
Suppose that we require a 12,5% return on new investments. We have an investment that costs $300 and has cash flow of $100 per year for five years. To get the discounted payback, we have to discount each cash flow at 12,5% and then start adding them.

19. 4.3. The Discounted Payback
Cash flow
Accumulated cash flow
Year
Undis-counted
Discoun- ted 1
100 89 2 79
200
168 3 70
300
238 4 62
400 5 55
500
355

20. 4.3. The Discounted Payback
We see that the regular payback is exactly three years. The discounted cash flows total $300 only after four years, so the discounted payback is four years.
How do we interpret the discounted payback?
We get our money back, along with the interest we could have earned elsewhere in four years.

21. 4.3. The Discounted Payback
Let’s compare the future value at 12.5% of the $300 investment to the future value of the $100 annual cash flows at 12.5%.
The two lines cross at exactly the fourth year.
Another interesting feature of the discounted payback period is that if a project ever pays back on a discounted basis, then it must have a positive NPV.

22. 4.3. The Discounted Payback

23. 4.3. The Discounted Payback
By definition, the NPV is zero when the sum of the discounted cash flows equals the initial investment. In our example, the present value of all cash flows is $355. The cost of the project was $300, so the NPV is obviously $55. This $55 is the value of the cash flow that occurs after the discounted payback.

24. 4.3. The Discounted Payback
The discounted payback is rarely used in practice, because it really isn’t any simpler to use than NPV.
Advantages of the Discounted Payback Period Rule:
1.Includes time value of money.
2.Easy to understand.
3.Does not accept negative estimated NPV investments.

25. 4.3. The Discounted Payback
4.Biased towards liquidity.
Disadvantages of the Discounted Payback Period Rule:
1.May reject positive NPV investments.
2.Requires an arbitrary cutoff point.

26. 4.3. The Discounted Payback
3.Ignores cash flows beyond the cutoff date.
4.Biased against long-term projects, such as research and development, and new projects.

27. 4.4. The Average Accounting Return
The average accounting return (AAR) is an investment’s average net income divided by its average book value.
The AAR is defined as:
Some measure of average accounting profit
Some measure of average accounting value
The specific definition we will use is:
Average net income
Average book value

28. 4.4. The Average Accounting Return
Suppose we are deciding whether to open a store in a new shopping mall or not. The required investment in improvements is $ The store would have a five-year life because everything reverts to the mall owners after that time.

29. 4.4. The Average Accounting Return
The required investment would be 100% depreciated (straight-line) over 5 years, so depreciation would be $ /5=$ per year. The tax rate is 25%. Table contains the projected revenues and expenses.

30. 4.4. The Average Accounting Return
Year
Revenue
Expenses
Earnings before
depreciation
Depreciation
Earnings before taxes
Taxes (25%)
Net income

31. 4.4. The Average Accounting Return
The average book value during the life of the investment is
($ ) / 2 = $ As long as we use straight-line depreciation, the average investment will always be one-half of the initial investment.
( )/6=250

32. 4.4. The Average Accounting Return
Net income is $ in the first year, $ in the second year, $ in the third year, $0 in year 4, and
in year 5.
The average net income is:
( – ) / 5=
= $50.000

33. 4.4. The Average Accounting Return
The average accounting return is:
If the firm has a target AAR less than 20%, then this investment is acceptable; otherwise it is not.

34. 4.4. The Average Accounting Return
Based on the average accounting return rule, a project is acceptable if its average accounting return exceeds a target average accounting return.

35. 4.4. The Average Accounting Return
Advantages of the Average Accounting Return:
1.Easy to calculate.
2.Needed information will usually be available.

36. 4.4. The Average Accounting Return
Disadvantages of the Average Accounting Return:
1.Not a true rate of return: time value of money is ignored.
2.Uses an arbitrary benchmark cutoff rate.
3.Based on accounting (book) values, not cash flows and market values.

37. 4.5. The Internal Rate Of Return
The internal rate of return (IRR) is the discounted rate that makes the NPV of an investment zero.
To illustrate the idea behind the IRR, consider a project that costs $100 today and pays $110 in one year. The return on this investment is 10% and is the internal rate of return, or IRR, on this investment.

38. 4.5. The Internal Rate Of Return
This project is a good investment if our required return is less than or equal to 10%.
Based on the IRR rule, an investment is acceptable if the IRR exceeds the required return. Otherwise it should be rejected.

39. 4.5. The Internal Rate Of Return
Imagine that we want to calculate the NPV for our simple investment.
At discount rate R, the NPV is:
NPV = - $ /(1+R)
Now, suppose we don’t know the discount rate. But we can still ask how high the discount rate would have to be before this project was deemed unacceptable.

40. 4.5. The Internal Rate Of Return
The investment is economically a break-even proposition when the NPV is zero because value is neither created nor destroyed. To find the break-even discount rate, we set NPV equal zero and solve for R:
NPV = 0 = -$ /(1+R)
100 = 110 / (1+R)
1+R = 110/100 =1,1
R = 10%

41. 4.5. The Internal Rate Of Return
The fact that the IRR is simply the discount rate that makes the NPV equal to zero is important because it tells us how to calculate the returns on more complicated investments.
Suppose the investment costs $100 and has a cash flow of $60 per year for two years.

42. 4.5. The Internal Rate Of Return
Year __________1___________2
We can set the NPV equal to zero and solve for the discount rate:
NPV=0= /(1+IRR)1 +60/(1+IRR)2
The only way to find the IRR in general is by trial and error.

43. 4.5. The Internal Rate Of Return
If we were to start with a 0%, the NPV would be $ = $20. At a 10% discount rate, we would have:
NPV=0= /(1,1)1+60/(1,1)2 =4,13
We can summarize these possibilities in a table. The NPV appears to be a zero with discount rate between 10% and 15%.
We can find that the IRR is 13,066239%.

44. 4.5. The Internal Rate Of Return
Discount rate
NPV 0%
20,00 5%
11,56
10%
4,13
15%
-2,46
20%
-8,33
To illustrate the
relationship between
NPV and IRR we plot
the numbers we
calculated.
We put the different
NPVs on the vertical
axis and the discount rates on the horizontal axis.

45. 4.5. The Internal Rate Of Return

46. 4.5. The Internal Rate Of Return
Net present value profile is a graphical representation of the relationship between an investment’s NPVs and various discount rates.

47. 4.5. The Internal Rate Of Return
The NPV rule and the IRR rule lead to identical accept-reject decisions. We will accept an investment using the IRR rule if the required return is less than 13,1%.
The NPV is positive at any discount rate less than 13,1%, so we would accept the investment using the NPV rule as well.

48. 4.5. The Internal Rate Of Return
The IRR and NPV rules always lead to identical decisions if two very important conditions are met.
1.The project cash flow must be conventional.
2.The project must be independent.

49. 4.5. The Internal Rate Of Return
Nonconventional cash flows
Suppose we have a strip-mining project that requires a $60 investment. Our cash flow in the first year will be $155. In the second year, the mine will be depleted, but we have to spent $100 to restore the terrain.
Year

50. 4.5. The Internal Rate Of Return
To find the IRR on this project, we can calculate the NPV at various rates:
Discount rate NPV
0% $5,00
,47
,28
,06
,31

51. 4.5. The Internal Rate Of Return
What’s the IRR? To find out, we draw the NPV profile.
The NPV is zero when the discount rate is 25% and the NPV is zero at 33,33%. Which of these is correct?
We see that the NPV is positive only if our required return is between 25% and 33,33%.

52. 4.5. The Internal Rate Of Return

53. 4.5. The Internal Rate Of Return
Descarte’s Rule of Sign says that the maximum number of IRRs that there can be is equal to the number of times that the cash flows change sign from positive to negative and/or negative to positive.
The actual number of IRRs can be less than the maximum.

54. 4.5. The Internal Rate Of Return- + -

55. 4.5. The Internal Rate Of Return- + -

56. 4.5. The Internal Rate Of Return- + + -

57. 4.5. The Internal Rate Of Return- + + -

58. 4.5. The Internal Rate Of Return- + + - -

59. 4.5. The Internal Rate Of Return+ - + - -

60. 4.5. The Internal Rate Of Return- + + - -

61. 4.5. The Internal Rate Of Return+ - + - + -

62. 4.5. The Internal Rate Of Return+ - + - + -

63. 4.5. The Internal Rate Of Return+ - + - + -

64. 4.5. The Internal Rate Of Return
Mutually exclusive investment decisions is a situation in which taking one investment prevents from taking another.
To illustrate the problem with the IRR rule and mutually exclusive investments, consider the following cash flows from two mutually exclusive investments:

65. 4.5. The Internal Rate Of Return
Year Investment A Investment B
$ $
IRR % %

66. 4.5. The Internal Rate Of Return
To see why investment A is not necessarily the better one of the two investments, we’ve calculated the NPV of these investments for different required returns:

67. 4.5. The Internal Rate Of Return
Discount rate NPV (A) NPV (B)
0% $ $
We see that the amount of NPV depends on our required return.

68. 4.5. The Internal Rate Of Return
The conflict between the IRR and NPV for mutually exclusive investments can be illustrated by plotting the investments’ NPV profiles.

69. 4.5. The Internal Rate Of Return

70. 4.5. The Internal Rate Of Return
The NPV profiles cross at about 11%. Notice that at any discount rate less than 11%, the NPV for B is higher. In this range, taking B benefits us more than taking A, even though A’s IRR is higher. At any rate greater than 11% Project A has the greater NPV.

71. 4.5. The Internal Rate Of Return
The crossover rate, by definition, is the discount rate that makes the NPVs of two projects equal. To illustrate, suppose we have following two mutually exclusive investments:
Year Investment A Investment B
__________________________________
$ $
What’s the crossover rate?

72. 4.5. The Internal Rate Of Return
NPVA = /(1+r) /(1+r)2
NPVB = (1+r) (1+r)2
NPVA = NPVB
/(1+r) /(1+r)2 = (1+r) (1+r)2
0 = /(1+r)1+ 60/(1+r)2

73. 4.5. The Internal Rate Of Return
0 = /(1+r)1+ 60/(1+r)2
We may find r by trial and error method. The r is exactly 20%. The two investments have the same value, so this 20% is the crossover rate. The NPV at 20% is $2,78 for both investments.

74. 4.5. The Internal Rate Of Return
Advantages of the Internal Rate of Return
1.Closely related to NPV, often leading to identical decisions.
2.Easy to understand and communicate.

75. 4.5. The Internal Rate Of Return
Disadvantages of the Internal Rate of Return
1.May result in multiple answers or not deal with nonconventional cash flows.
2.May lead to incorrect decisions in comparison of mutually exclusive investments.

76. 4.5. The Internal Rate Of Return
The profitability index (PI), or benefit-cost ratio.
This index is defined as the future cash flows divided by the initial investment.
So, if a project costs $200 and the present value of its future cash flows is $220, the profitability index value would be:
PI = $220/200 =1,1
Notice, that the NPV for this investment is $20.

77. 4.5. The Internal Rate Of Return
The PI is obviously very similar to NPV. However, consider the two investments:
Investment A B
Costs $5
$100
Present value
$10
$150 PI 2
1,5
NPV
$50

78. 4.5. The Internal Rate Of Return
Advantages of the Profitability Index
1.Closely related to NPV, generally leading to identical decisions.
2.Easy to understand and communicate.
3.May be useful when available investment funds are limited.

79. 4.5. The Internal Rate Of Return
Disadvantages of the Profitability Index
1.May lead to incorrect decisions in comparison with mutually exclusive investments.